Ed Miliband has said the Labour party must offer a new national mission to win back voters who deserted them for the Conservatives.

In a speech to the Progress thinktank in London, Miliband pledged to tackle the "new inequality" between the rich and the rest of society, but also admitted the gap had grown under the last Labour government.

The party would only succeed in regaining power if it could counter the "shrivelled, pessimistic, austere" vision of David Cameron and the Conservatives, he said.

In a direct pitch to middle-class voters in the south of England, Miliband said their living standards were being squeezed in the same way as those in poorer parts of the country.

Labour needed the humility to acknowledge that the inequality between "those at the top and everyone else" had grown under the last Labour government, although the coalition was exacerbating the problem.

"Inequality is no longer an issue just between rich and poor. But between those at the top and those both in the middle and on lower incomes," he said.

"Since 2003, those at the top have seen their living standards continue to rise at extraordinary rates, while those of the rest have stagnated.

"This is about the middle-income people in the south of England and elsewhere who don't consider themselves rich even though they may be higher-rate taxpayers."

Miliband said the recent local elections showed that the party was winning back disaffected Liberal Democrat voters who felt betrayed by their leadership, but it had yet to make inroads into the Conservative vote.

To win back those former Labour voters, the party needed to own up to its past mistakes, including being too relaxed about the impact of cheap migrant labour on wages, he said.

"Eastern European immigration did place downward pressure on wages. People can argue about the extent. We were too relaxed about that."

Miliband offered little policy detail in his speech, focusing instead on his broad vision of how Labour would approach the next general election.

He attacked what he said was the Conservatives' "almost Maoist contempt" for any institution that did not conform to their ideological beliefs.

"That's why they tried to sell off our ancient forests. It's why [universities minister] David Willetts saw nothing wrong with the suggestion that the wealthy should be able to buy their way into university," he said.

However he warned that the party could not afford to simply "hunker down and benefit from an unpopular government".

"I hear it quite a lot – let's be a louder, prouder opposition," he said. "But to think that is enough is to fail to understand the depth of the loss of trust in us and the scale of change required to win it back."

He said he was committed to tackling Britain's budget deficit, but that the current government's austerity measures were loading more of the financial burden on to those who were already struggling.

Improving jobs and wages would mean "asking less of the state", although he did not eloborate on whether this meant something akin to Cameron's "big society".

"The truth is that we cannot create a society that is equal to the aspirations of the British people in a world of wide and growing inequalities – a world in which there are bailouts for bankers and austerity for the rest.

"Asking more of our economy, good jobs and wages, means asking less of the state. At times, we hung on to a picture of Britain in which people were either poor, and desperately in need of our help, or affluent, aspirational, and doing OK.

"We failed to understand that for millions of people in the middle, life was becoming more and more difficult.

"In the future the Labour offer to aspirational voters must be that we will address the new inequality by hard-wiring fairness into the economy."

The Conservative party deputy chairman, Michael Fallon, dismissed the speech, saying the Labour leader had failed to set out a credible alternative.

"He says the public want more from his party and he's right, they want to know his plan to deal with the appalling deficit that the last Labour government left the country," he said.

Gavin Kelly, deputy chief of staff in Downing Street from 2007-2010 and now chief executive of the Resolution Foundation, explains why solving the problems of the 'squeezed middle' will change British politics